A148319 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 1), (-1, 0, 1), (-1, 1, 1), (0, 0, 1), (1, 0, -1)}.

1, 1, 2, 5, 14, 39, 126, 396, 1362, 4639, 16619, 59519, 220100, 815414, 3090682, 11738378, 45353386, 175598040, 688854841, 2708282490, 10756657528, 42820338694, 171830989992, 691099456497, 2797481451289, 11348882879661, 46281865516679, 189139996758076, 776311395758161, 3192648976527350

Offset

0,3

Links

Table of n, a(n) for n=0..29.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A148316 A148317 A148318 * A126219 A320568 A111110

Adjacent sequences: A148316 A148317 A148318 * A148320 A148321 A148322

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved